Designing a Brain Computer Interface (BCI) system one can choose from a variety of features that
may be useful for classifying brain activity during a mental task. For the special case of classifying EEG signals we propose the usage of the state of the art feature selection algorithms Recursive Feature Elimination [3] and Zero-Norm Optimization [13] which are based on the training of Support Vector Machines (SVM) [11]. These algorithms can provide more accurate solutions than standard filter methods for feature selection [14].
We adapt the methods for the purpose of selecting EEG channels. For a motor imagery paradigm we
show that the number of used channels can be reduced significantly without increasing the classification error. The resulting best channels agree well with the expected underlying cortical activity patterns during the mental tasks.
Furthermore we show how time dependent task specific information can be visualized.

In a number of models of depth cue combination the depth percept is constructed via a weighted average combination of independent depth estimations. The influence of each cue in such average depends on the reliability of the source of information. (Young, Landy, & Maloney, 1993; Ernst & Banks, 2002.) In particular, Ernst & Banks (2002) formulate the combination performed by the human brain as that of the minimum variance unbiased estimator that can be constructed from the available cues.
Using slant discrimination and slant judgment via probe adjustment as tasks, we have observed systematic differences in performance of human observers when a number of different types of textures were used as cue to slant (Rosas, Wichmann & Wagemans, 2003). If the depth percept behaves as described above, our measurements of the slopes of the psychometric functions provide the predicted weights for the texture cue for the ranked texture types. We have combined these texture types with object motion but the obtained results are difficult to reconcile with the unbiased minimum variance estimator model (Rosas & Wagemans, 2003). This apparent failure of such model might be explained by the existence of a coupling of texture and motion, violating the assumption of independence of cues. Hillis, Ernst, Banks, & Landy (2002) have shown that while for between-modality combination the human visual system has access to the single-cue information, for within-modality combination (visual cues: disparity and texture) the single-cue information is lost, suggesting a coupling between these cues. Then, in the present study we combine the different texture types with haptic information in a slant discrimination task, to test whether in the between-modality condition the texture cue and the haptic cue to slant are combined as predicted by an unbiased, minimum variance estimator model.

We obtain exponential concentration inequalities for sub-additive
functions of independent random variables under weak conditions on the
increments of those functions, like
the existence of exponential moments for these increments.
As a consequence of these general inequalities, we obtain refinements
of Talagrand's inequality for empirical processes and new
bounds for randomized empirical processes.
These results are obtained by further developing the entropy method
introduced by Ledoux.

We investigate data based procedures for selecting the kernel when learning with Support Vector Machines. We provide generalization error bounds by estimating the Rademacher complexities of the corresponding function classes. In particular we obtain a complexity bound for function classes induced by kernels with given eigenvectors, i.e., we allow to vary the spectrum and keep the eigenvectors fix. This bound is only a logarithmic factor bigger than the complexity of the function class induced by a single kernel. However, optimizing the margin over such classes leads to overfitting. We thus propose a suitable way of constraining the class. We use an efficient algorithm to solve the resulting optimization problem, present preliminary experimental results, and compare them
to an alignment-based approach.

We propose a framework to incorporate unlabeled data in kernel
classifier, based on the idea that two points in the same cluster are more likely to have the same label. This is achieved by modifying the eigenspectrum of the kernel matrix. Experimental results assess the validity of this approach.

We introduce a class of string kernels, called mismatch kernels, for use with support vector machines (SVMs) in a discriminative approach to the protein classification problem. These kernels measure sequence similarity
based on shared occurrences of k-length subsequences, counted with up to m mismatches, and do not rely on any generative model for the positive training sequences. We compute the kernels efficiently using a mismatch tree data structure and report experiments on a benchmark SCOP dataset, where we show that the mismatch kernel used with an SVM classifier performs as well as the Fisher kernel, the most successful method for remote homology detection, while achieving considerable computational savings.

The tangential neurons in the fly brain are sensitive to the typical optic flow patterns generated during self-motion. In this study, we examine whether a simplified linear model of these neurons can be used to estimate self-motion from the optic flow. We present a theory for
the construction of an estimator consisting of a linear combination of optic flow vectors that incorporates prior knowledge both about the distance distribution of the environment, and about the noise and self-motion statistics of the sensor. The estimator is tested on a gantry carrying an omnidirectional vision sensor. The experiments show
that the proposed approach leads to accurate and robust estimates of rotation rates, whereas translation estimates turn out to be less reliable.

Recently the Fisher score (or the Fisher kernel) is increasingly used as a feature extractor for classification problems. The Fisher score is a vector of parameter derivatives of loglikelihood of a probabilistic model. This
paper gives a theoretical analysis about how class information is preserved in the space of the Fisher score, which turns out that the Fisher score consists of a few important dimensions with class information and many nuisance dimensions. When we perform clustering with the Fisher score, K-Means type methods are obviously inappropriate because they make use of all dimensions. So we will develop a novel but simple clustering
algorithm specialized for the Fisher score, which can exploit important dimensions. This algorithm is successfully tested in experiments with artificial data and real data (amino acid sequences).

Gaussian Process (GP) inference is a probabilistic kernel method where the GP is treated as a latent function. The inference is carried out using the Bayesian online learning and its extension to the more general iterative approach which we call TAP/EP learning.
Sparsity is introduced in this context to make the TAP/EP method applicable to large datasets. We address the prohibitive scaling of the number of parameters by defining a subset of the training data that is used as the support the GP, thus the number of required parameters is independent of the training set, similar to the case of ``Support--‘‘ or ``Relevance--Vectors‘‘.
An advantage of the full probabilistic treatment is that allows the computation of the marginal data likelihood or evidence, leading to hyper-parameter estimation within the GP inference.
An EM algorithm to choose the hyper-parameters is proposed. The TAP/EP learning is the E-step and the M-step then updates the hyper-parameters. Due to the sparse E-step the resulting algorithm does not involve manipulation of large matrices. The presented algorithm is applicable to a wide variety of likelihood functions. We present results of applying the algorithm on classification and nonstandard regression problems for artificial and real datasets.

In Proceedings of the 13th IFAC Symposium on System Identification, pages: 1195-1200, (Editors: Van den Hof, P., B. Wahlberg and S. Weiland), Proceedings of the 13th IFAC Symposium on System Identification, August 2003 (inproceedings)

Abstract

Nonparametric Gaussian Process models, a Bayesian statistics approach, are used to implement a nonlinear adaptive control law. Predictions, including propagation of the state uncertainty are made over a k-step horizon. The expected value of a quadratic cost function is minimised, over this prediction horizon, without ignoring the variance of the model predictions. The general method and its main features are illustrated on a simulation example.

In this paper we present a learning-based approach for the modelling of complex movement sequences. Based on the method of Spatio-Temporal Morphable Models (STMMS. We derive a hierarchical algorithm that, in a first step, identifies automatically movement elements in movement sequences based on a coarse spatio-temporal description, and in a second step models these movement primitives by approximation through linear combinations of learned example movement trajectories. We describe the different steps of the algorithm and show how it can be applied for modelling and synthesis of complex sequences of human movements that contain movement elements with variable style. The proposed method is demonstrated on different applications of movement representation relevant for imitation learning of movement styles in humanoid robotics.

We give an exposition of the ideas of statistical learning theory, followed by a discussion of how a reinterpretation of the insights of learning theory could potentially also benefit our understanding of a certain notion of complexity.

The Google search engine has had a huge success with its PageRank
web page ranking algorithm, which exploits global, rather than
local, hyperlink structure of the World Wide Web using random
walk. This algorithm can only be used for graph data, however.
Here we propose a simple universal ranking algorithm for vectorial
data, based on the exploration of the intrinsic global geometric
structure revealed by a huge amount of data. Experimental results
from image and text to bioinformatics illustrates the validity of
our algorithm.

A new method for performing a kernel principal component analysis is
proposed. By kernelizing the generalized Hebbian algorithm, one can
iteratively estimate the principal components in a reproducing
kernel Hilbert space with only linear order memory complexity. The
derivation of the method, a convergence proof, and preliminary
applications in image hyperresolution are presented. In addition,
we discuss the extension of the method to the online learning of
kernel principal components.

We consider the learning problem in the transductive setting. Given
a set of points of which only some are labeled, the goal is to
predict the label of the unlabeled points. A principled clue to
solve such a learning problem is the consistency assumption that a
classifying function should be sufficiently smooth with respect to
the structure revealed by these known labeled and unlabeled points. We present a simple
algorithm to obtain such a smooth solution. Our method yields encouraging experimental results on a
number of classification problems and demonstrates effective use of
unlabeled data.

Annals of the Institute of Statistical Mathematics, 55(2):391-408, June 2003 (article)

Abstract

In kernel methods, all the information about the training data is contained in the Gram matrix. If this matrix has large diagonal values, which arises for many types of kernels, then kernel methods do not perform well: We propose and test several methods for dealing with this problem by reducing the dynamic range of the matrix while preserving the positive definiteness of the Hessian of the quadratic programming problem that one has to solve when training a Support Vector Machine, which is a common kernel approach for pattern recognition.

The Wiener series is one of the standard methods to systematically
characterize the nonlinearity of a neural system. The classical
estimation method of the expansion coefficients via cross-correlation
suffers from severe problems that prevent its application to
high-dimensional and strongly nonlinear systems. We propose a new
estimation method based on regression in a reproducing kernel Hilbert
space that overcomes these problems. Numerical experiments show
performance advantages in terms of convergence, interpretability and
system size that can be handled.

A key tool in protein function discovery is the ability to rank databases of proteins given a query amino acid sequence. The most successful method so far is a web-based tool called PSI-BLAST which uses heuristic alignment of a profile built using the large unlabeled database. It has been shown that such use of global information via an unlabeled data improves over a local measure derived from a basic pairwise alignment such as performed by PSI-BLAST's predecessor, BLAST. In this article we
look at ways of leveraging techniques from the field of machine learning for the problem of ranking. We show how clustering and semi-supervised learning techniques, which aim to capture global structure in data, can significantly improve over PSI-BLAST.

We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinearized variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher‘s discriminant and oriented PCA using support vector kernel functions. Extensive simulations show the utility of our approach.

Canonical correlation analysis (CCA) is a classical multivariate method concerned with describing linear dependencies between sets of variables. After a short exposition of the linear sample CCA problem and its analytical solution, the article proceeds with a detailed characterization of its geometry. Projection operators are used to illustrate the relations between canonical vectors and variates. The article then addresses the problem of CCA between spaces spanned by objects mapped into kernel feature spaces. An exact solution for this kernel canonical correlation (KCCA) problem is derived from a geometric point of view. It shows that the expansion coefficients of the canonical vectors in their respective feature space can be found by linear CCA in the basis induced by kernel principal component analysis. The effect of mappings into higher dimensional feature spaces is considered critically since it simplifies the CCA problem in general. Then two regularized variants of KCCA are discussed. Relations to other methods are illustrated, e.g., multicategory kernel Fisher discriminant analysis, kernel principal component regression and possible applications thereof in blind source separation.

In Proceedings of the International Conference on Intelligent Control Systems and Signal Processing ICONS 2003, 1, pages: 137-142, (Editors: Ruano, E.A.), Proceedings of the International Conference on Intelligent Control Systems and Signal Processing ICONS, April 2003 (inproceedings)

Abstract

In this paper an alternative approach to black-box identification of non-linear dynamic systems is compared with the more established approach of using artificial neural networks. The Gaussian process prior approach is a representative of non-parametric modelling approaches. It was compared on a pH process modelling case study. The purpose of modelling was to use the model for control design. The comparison revealed that even though Gaussian process models can be effectively used for modelling dynamic systems caution has to be axercised when signals are selected.

In this paper, we describe an efficient algorithm to sequentially update a density support estimate obtained using one-class support vector machines. The solution provided is an exact solution, which proves to be far more computationally attractive than a batch approach. This deterministic technique is applied to the problem of audio signal segmentation, with simulations demonstrating the computational performance gain on toy data sets, and the accuracy of the segmentation on audio signals.

We introduce two new functions, the kernel covariance (KC) and the kernel
mutual information (KMI), to measure the degree of independence of several
continuous random variables.
The former is guaranteed to be zero if and only if the random variables
are pairwise independent; the latter shares this property, and is in addition
an approximate upper bound on the mutual information, as measured near
independence, and is based on a kernel density estimate.
We show that Bach and Jordan‘s kernel generalised variance (KGV) is also
an upper bound on the same kernel density estimate, but is looser.
Finally, we suggest that the addition of a regularising term in the KGV
causes it to approach the KMI, which motivates the introduction of this
regularisation.
The performance of the KC and KMI is verified in the context of instantaneous
independent component analysis (ICA), by recovering both artificial and
real (musical) signals following linear mixing.

We introduce a new contrast function, the kernel mutual information
(KMI), to measure the degree of independence of continuous random
variables. This contrast function provides an approximate upper bound
on the mutual information, as measured near independence, and is based
on a kernel density estimate of the mutual information between a discretised
approximation of the continuous random variables. We show that Bach
and Jordan&lsquo;s kernel generalised variance (KGV) is also an upper bound
on the same kernel density estimate, but is looser. Finally, we suggest
that the addition of a regularising term in the KGV causes it to approach
the KMI, which motivates the introduction of this regularisation.

Motivation: In drug discovery a key task is to identify characteristics that separate active (binding) compounds from inactive (non-binding) ones. An automated prediction system can help reduce resources necessary to carry out this task.
Results: Two methods for prediction of molecular bioactivity for drug design are introduced and shown to perform well in a data set previously studied as part of the KDD (Knowledge Discovery and Data Mining) Cup 2001. The data is characterized by very few positive examples, a very large number of features (describing three-dimensional properties of the molecules) and rather different distributions between training and test data. Two techniques are introduced specifically to tackle these problems: a feature selection method for unbalanced data and a classifier which adapts to the distribution of the the unlabeled test data (a so-called transductive method). We show both techniques improve identification performance and in conjunction provide an improvement over using only one of the techniques. Our results suggest the importance of taking into account the characteristics in this data which may also be relevant in other problems of a similar type.

In The International Symposium on Adaptive Motion of Animals and Machines, Kyoto, Japan, March 4-8, 2003, March 2003, clmc (inproceedings)

Abstract

Sensory-motor integration is one of the key issues in robotics. In this paper, we propose an approach to rhythmic arm movement control that is synchronized with an external signal based on exploiting a simple neural oscillator network. Trajectory generation by the neural oscillator is a biologically inspired method that can allow us to generate a smooth and continuous trajectory. The parameter tuning of the oscillators is used to generate a synchronized movement with wide intervals. We adopted the method for the drumming task as an example task. By using this method, the robot can realize synchronized drumming with wide drumming intervals in real time. The paper also shows the experimental results of drumming by a humanoid robot.

We explore the use of the so-called zero-norm of the parameters of linear models in learning. Minimization of such a quantity has many uses in a machine learning context: for variable or feature selection, minimizing training error and ensuring sparsity in solutions. We derive a simple but practical method for achieving these goals and discuss its relationship to existing techniques of minimizing the zero-norm. The method boils down to implementing a simple modification of vanilla SVM, namely via an iterative multiplicative rescaling of the training data. Applications we investigate which aid our discussion include variable and feature selection on biological microarray data, and multicategory classification.

Fourier phase plays an important role in determining image structure. For example,
when the phase spectrum of an image showing a
ower is swapped with the phase
spectrum of an image showing a tank, then we will usually perceive a tank in the
resulting image, even though the amplitude spectrum is still that of the
ower. Also,
when the phases of an image are randomly swapped across frequencies, the resulting
image becomes impossible to recognize. Our goal was to evaluate the eect of phase
manipulations in a more quantitative manner. On each trial subjects viewed two images
of natural scenes. The subject had to indicate which one of the two images contained
an animal. The spectra of the images were manipulated by adding random phase noise
at each frequency. The phase noise was uniformly distributed in the interval [;+],
where was varied between 0 degree and 180 degrees. Image pairs were displayed for
100 msec. Subjects were remarkably resistant to the addition of phase noise. Even with
[120; 120] degree noise, subjects still were at a level of 75% correct. The introduction
of phase noise leads to a reduction of image contrast. Subjects were slightly better
than a simple prediction based on this contrast reduction. However, when contrast
response functions were measured in the same experimental paradigm, we found that
performance in the phase noise experiment was signicantly lower than that predicted
by the corresponding contrast reduction.

Using robots as models of cognitive behaviour has a long tradition in robotics. Parallel to the historical development in cognitive science, one observes two major, subsequent waves in cognitive robotics. The first is based on ideas of classical, cognitivist Artificial Intelligence (AI). According to the AI view of cognition as rule-based symbol manipulation, these robots typically try to extract symbolic descriptions of the environment from their sensors that are used to update a common, global world representation from which, in turn, the next action of the robot is derived. The AI approach has been successful in strongly restricted and controlled environments requiring well-defined tasks, e.g. in industrial assembly lines.
AI-based robots mostly failed, however, in the unpredictable and unstructured environments that have to be faced by mobile robots. This has provoked the second wave in cognitive robotics which tries to achieve cognitive behaviour as an emergent property from the interaction of simple, low-level modules. Robots of the second wave are called animats as their architecture is designed to closely model aspects of real animals. Using only simple reactive mechanisms and Hebbian-type or evolutionary learning, the resulting animats often outperformed the highly complex AI-based robots in tasks such as obstacle avoidance, corridor following etc.
While successful in generating robust, insect-like behaviour, typical animats are limited to stereotyped, fixed stimulus-response associations. If one adopts the view that cognition requires a flexible, goal-dependent choice of behaviours and planning capabilities (H.A. Mallot, Kognitionswissenschaft, 1999, 40-48) then it appears that cognitive behaviour cannot emerge from a collection of purely reactive modules. It rather requires environmentally decoupled structures that work without directly engaging the actions that it is concerned with. This poses the current challenge to cognitive robotics: How can we build cognitive robots that show the robustness and the learning capabilities of animats without falling back into the representational paradigm of AI?
The speakers of the symposium present their approaches to this question in the context of robot navigation and sensorimotor learning. In the first talk, Prof. Helge Ritter introduces a robot system for imitation learning capable of exploring various alternatives in simulation before actually performing a task. The second speaker, Angelo Arleo, develops a model of spatial memory in rat navigation based on his electrophysiological experiments. He validates the model on a mobile robot which, in some navigation tasks, shows a performance comparable to that of the real rat. A similar model of spatial memory is used to investigate the mechanisms of territory formation in a series of robot experiments presented by Prof. Hanspeter Mallot. In the last talk, we return to the domain of sensorimotor learning where Ralf M{\"o}ller introduces his approach to generate anticipatory behaviour by learning forward models of sensorimotor relationships.

Imitation learning is frequently discussed as a method for generating complex behaviors
in robots by imitating human actors. The kinematic and the dynamic properties of
humans and robots are typically quite dierent, however. For this reason observed
human trajectories cannot be directly transferred to robots, even if their geometry is
humanoid. Instead the human trajectory must be approximated by trajectories that
can be realized by the robot. During this approximation deviations from the human
trajectory may arise that change the style of the executed movement. Alternatively, the
style of the movement might be well reproduced, but the imitated trajectory might be
suboptimal with respect to dierent constraint measures from robotics control, leading
to non-robust behavior. Goal of the presented work is to quantify this trade-o between
\imitation quality" and constraint compatibility for the imitation of complex writing
movements. In our experiment, we used trajectory data from human writing movements
(see the abstract of Ilg et al. in this volume). The human trajectories were mapped
onto robot trajectories by minimizing an error measure that integrates constraints that
are important for the imitation of movement style and a regularizing constraint that
ensures smooth joint trajectories with low velocities. In a rst experiment, both the
end-eector position and the shoulder angle of the robot were optimized in order to
achieve good imitation together with accurate control of the end-eector position. In
a second experiment only the end-eector trajectory was imitated whereas the motion
of the elbow joint was determined using the optimal inverse kinematic solution for the
robot. For both conditions dierent constraint measures (dexterity and relative jointlimit
distances) and a measure for imitation quality were assessed. By controling the
weight of the regularization term we can vary continuously between robot behavior
optimizing imitation quality, and behavior minimizing joint velocities.

We attempt to reach a better understanding of classication in humans using both
psychophysical and machine learning techniques. In our psychophysical paradigm the
stimuli presented to the human subjects are modied using machine learning algorithms
according to their responses. Frontal views of human faces taken from a processed
version of the MPI face database are employed for a gender classication task. The
processing assures that all heads have same mean intensity, same pixel-surface area
and are centered. This processing stage is followed by a smoothing of the database
in order to eliminate, as much as possible, scanning artifacts. Principal Component
Analysis is used to obtain a low-dimensional representation of the faces in the database.
A subject is asked to classify the faces and experimental parameters such as class (i.e.
female/male), condence ratings and reaction times are recorded. A mean classication
error of 14.5% is measured and, on average, 0.5 males are classied as females
and 21.3females as males. The mean reaction time for the correctly classied faces is
1229 +- 252 [ms] whereas the incorrectly classied faces have a mean reaction time of
1769 +- 304 [ms] showing that the reaction times increase with the subject's classi-
cation error. Reaction times are also shown to decrease with increasing condence,
both for the correct and incorrect classications. Classication errors, reaction times
and condence ratings are then correlated to concepts of machine learning such as
separating hyperplane obtained when considering Support Vector Machines, Relevance
Vector Machines, boosted Prototype and K-means Learners. Elements near the separating
hyperplane are found to be classied with more errors than those away from
it. In addition, the subject's condence increases when moving away from the hyperplane.
A preliminary analysis on the available small number of subjects indicates that
K-means classication seems to re
ect the subject's classication behavior best. The
above learnersare then used to generate \special" elements, or representations, of the
low-dimensional database according to the labels given by the subject. A memory experiment
follows where the representations are shown together with faces seen or unseen
during the classication experiment. This experiment aims to assess the representations
by investigating whether some representations, or special elements, are classied
as \seen before" despite that they never appeared in the classication experiment,
possibly hinting at their use during human classication.

Imitation learning of complex movements has become a popular topic in neuroscience,
as well as in robotics. A number of conceptual as well as practical problems are still
unsolved. One example is the determination of the aspects of movements which are
relevant for imitation. Problems concerning the movement representation are twofold:
(1) The movement characteristics of observed movements have to be transferred from
the perceptual level to the level of generated actions. (2) Continuous spaces of movements
with variable styles have to be approximated based on a limited number of
learned example sequences. Therefore, one has to use representation with a high generalisation
capability. We present methods for the representation of complex movement
sequences that addresses these questions in the context of the imitation learning of
writing movements using a robot arm with human-like geometry. For the transfer of
complex movements from perception to action we exploit a learning-based method that
represents complex action sequences by linear combination of prototypical examples (Ilg
and Giese, BMCV 2002). The method of hierarchical spatio-temporal morphable models
(HSTMM) decomposes action sequences automatically into movement primitives.
These primitives are modeled by linear combinations of a small number of learned
example trajectories. The learned spatio-temporal models are suitable for the analysis
and synthesis of long action sequences, which consist of movement primitives with
varying style parameters. The proposed method is illustrated by imitation learning
of complex writing movements. Human trajectories were recorded using a commercial
motion capture system (VICON). In the rst step the recorded writing sequences
are decomposed into movement primitives. These movement primitives can be analyzed
and changed in style by dening linear combinations of prototypes with dierent
linear weight combinations. Our system can imitate writing movements of dierent
actors, synthesize new writing styles and can even exaggerate the writing movements
of individual actors. Words and writing movements of the robot look very natural, and
closely match the natural styles. These preliminary results makes the proposed method
promising for further applications in learning-based robotics. In this poster we focus
on the acquisition of the movement representation (identication and segmentation of
movement primitives, generation of new writing styles by spatio-temporal morphing).
The transfer of the generated writing movements to the robot considering the given
kinematic and dynamic constraints is discussed in Bakir et al (this volume).

The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables improved estimates of forecasted values and their uncertainties. In this paper we focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian Process and the Relevance Vector Machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods.

In The 3rd International Workshop on Statistical and Computational Theories of Vision (SCTV 2003), pages: 1-24, 3rd International Workshop on Statistical and Computational Theories of Vision (SCTV), 2003 (inproceedings)

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems